In part, the disclosure relates to methods of stent strut detection relative to a side branch region using intravascular data. In one embodiment, detecting stent struts relative to jailed side branches is performed using a scan line-based peak analysis. In one embodiment, false positive determinations relating to stent struts are analyzed using a model strut.
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1. A method of detecting one or more stent struts disposed in a side branch, the method comprising:
storing, in memory accessible by a diagnostic system, one or more image datasets obtained with respect to a blood vessel;
detecting, using a side branch detection module of the diagnostic system, one or more side branches of the blood vessel using the one or more image datasets;
identifying side branch image data corresponding to each detected side branch, wherein each side branch has a shadow region;
determining one or more candidate intensity peaks relative to one or more shadow regions; and
validating the one or more candidate intensity peaks, wherein each valid intensity peak corresponds to a portion of a stent strut jailing one or more side branches.
10. An automatic processor-based diagnostic system for detecting one or more stent struts disposed in a side branch, the system comprising:
one or more memory devices; and
a computing device in communication with the memory device, wherein the memory device comprises instructions executable by the computing device to cause the computing device to:
store, in the one or more memory devices, one or more image datasets obtained with respect to a blood vessel;
detect, using a side branch detection module of the diagnostic system, one or more side branches of the blood vessel using the one or more image datasets;
identify side branch image data corresponding to each detected side branch, wherein each side branch has a shadow region;
determine one or more candidate intensity peaks relative to one or more shadow regions; and
validate the one or more candidate intensity peaks, wherein each valid intensity peak corresponds to a portion of a stent strut jailing one or more side branches.
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This application is a continuation of U.S. patent application Ser. No. 14/975,462, filed on Dec. 18, 2015, which claims priority to and the benefit of U.S. Provisional Patent Application No. 62/257,185 filed on Nov. 18, 2015, the disclosures of which are herein incorporated by reference in their entirety.
The invention relates to systems and methods for stent detection.
Interventional cardiologists incorporate a variety of diagnostic tools during catheterization procedures in order to plan, guide, and assess therapies. Fluoroscopy is generally used to perform angiographic imaging of blood vessels. In turn, such blood vessel imaging is used by physicians to diagnose, locate and treat blood vessel disease during interventions such as bypass surgery or stent placement. Intravascular imaging technologies such as optical coherence tomography (OCT) are also valuable tools that can be used in lieu of or in combination with fluoroscopy to obtain high-resolution data regarding the condition of the blood vessels for a given subject.
Intravascular optical coherence tomography is a catheter-based imaging modality that uses light to peer into coronary artery walls and generate images for study. Utilizing coherent light, interferometry, and micro-optics, OCT can provide video-rate in-vivo tomography within a diseased vessel with micrometer level resolution. Viewing subsurface structures with high resolution using fiber-optic probes makes OCT especially useful for minimally invasive imaging of internal tissues and organs, as well as implanted medical devices such as stents.
Stents are a common intervention for treating vascular stenoses. It is critical for a clinician to develop a personalized stent plan that is customized to the patient's vascular anatomy to ensure optimal outcomes in intravascular procedures. Stent planning encompasses selecting the length, diameter, and landing zone for the stent with an intention to restore normal blood flow to the downstream tissues. However, flow-limiting stenoses are often present in the vicinity of vascular side branches. Side branches can be partially occluded or “jailed” during deployment of a stent intended to address a stenosis in the main vessel. Since side branches are vital for carrying blood to downstream tissues, jailing can have an undesired ischemic impact and also can lead to thrombosis. The ischemic effects of jailing are compounded when multiple side branches are impacted or when the occluded surface area of a single branch is increased.
Metal stent detection methods typically detect individual stent struts by detecting shadows cast by the struts onto the blood vessel wall, followed by detecting the location of the struts within the detected shadows. However, struts over jailed side branches are difficult to detect via this method. Side branches appear as large shadows in images because the scan line can be perpendicular to the side branch opening. As a result, it is difficult or impossible to detect strut shadows overlying side branches. Consequently, jailing struts are easily missed by the shadow based detection methods.
The present disclosure addresses the need for enhanced detection of jailing stent struts.
Disclosed herein are systems and methods for detecting and visualizing stent struts that occlude, or jail, blood vessel side branches. The systems and methods disclosed herein detect jailing struts by analyzing side branches for sparse intensity peaks. In one embodiment, sparse intensity peaks include scan line intensity peaks that are surrounded by dark regions. The sparse intensity peaks can be identified on optical coherence tomography (OCT) scan lines. The peak corresponds to a potential strut, and the dark regions correspond to the underlying side branch lumen, which appears as a void. Scan lines with potential strut peaks are analyzed to determine whether the scan lines fit an intensity profile consistent with a jailing strut. In one embodiment, consecutive scan lines with potential strut peaks are analyzed to determine whether the scan lines fit an intensity profile consistent with a jailing strut.
In one embodiment, the systems and methods described herein identify a side branch and identify a potential strut at a particular location within the side branch. In one embodiment, the particular location is line-offset. The system and associated side branch detection or other associated software module can then create a model strut at that same location.
In part, the disclosure relates to a method of detecting a stent strut in a representation of a blood vessel. The method includes storing, in memory accessible by an intravascular diagnostic system, intravascular data comprising a first group of scan lines; detecting side branches in the intravascular data; identifying a second group of scan lines within one or more of the detected side branches; determining a peak intensity for each scan line in the second group of scan lines; identifying a third group of scan lines in the second group having a peak intensity less than or equal to a threshold T, wherein the third group comprises one or more scan lines of a detected side branch that are candidates for comprising stent strut image data; and validating the candidates to identify one or more scan lines that comprise stent strut data.
In one embodiment, the validating step comprises determining if each candidate is a false positive for comprising stent strut image data. In one embodiment, the validating step comprises comparing the candidate stent strut image data to model stent strut image data using a correlation factor. In one embodiment, the correlation factor is a linear correlation coefficient. In one embodiment, determining if each candidate is a false positive for comprising stent strut image data comprises comparing the detected candidate stent strut image data to model stent strut image data.
In one embodiment, after determining a peak intensity for each scan line, the method comprises a partitioning the scan lines for a side branch into samples. In one embodiment, the method further includes a step of clustering neighboring scan lines that are contiguous, before validating against the model strut.
In one embodiment, the method further includes the step of adding a validated strut to a list of detected struts. In one embodiment, if the number of samples having an intensity>peak-at-line intensity is greater than threshold T for a candidate strut, discarding the candidate strut or the scan line comprising the candidate strut. In one embodiment, the method further includes determining a start frame and an end frame for each side branch.
In part, the disclosure relates to an automatic processor-based system for detecting a stent strut in a representation of a blood vessel. The system includes one or more memory devices; and a computing device in communication with the memory device, wherein the memory device comprises instructions executable by the computing device to cause the computing device to: store, in memory accessible by an intravascular diagnostic system, intravascular data comprising a first group of scan lines; detect side branches in the intravascular data; identify a second group of scan lines within one or more of the detected side branches; determine a peak intensity for each scan line in the second group of scan lines; identify a third group of scan lines in the second group having a peak intensity less than or equal to a threshold T, wherein the third group comprises one or more scan lines of a detected side branch that are candidates for comprising stent strut image data; and validate the candidates to identify one or more scan lines that comprise stent strut data. instructions to validate step comprises determining if each candidate is a false positive for comprising stent strut image data.
In one embodiment, the method includes instructions to validate step comprises comparing the candidate stent strut image data to model stent strut image data using a correlation factor. In one embodiment, the correlation factor is a linear correlation coefficient. In one embodiment, the computing device comprises further instructions to cause the computing device to determine if each candidate is a false positive for comprising stent strut image data comprises comparing the detected candidate stent strut image data to model stent strut image data. In one embodiment, after determining a peak intensity for each scan line, the computing device comprises further instructions to cause the computing device to partition the scan lines for a side branch into samples.
In one embodiment, the computing device comprises further instructions to cause the computing device to cluster neighboring scan lines that are contiguous, before validating against the model strut. In one embodiment, the computing device comprises further instructions to cause the computing device to adding a validated strut to a list of detected struts.
In one embodiment, if the number of samples having an intensity>peak-at-line intensity is greater than threshold T for a candidate strut, discarding the candidate strut or the scan line comprising the candidate strut. In one embodiment, the computing device comprises further instructions to cause the computing device to determine a start frame and an end frame for each side branch.
The figures are not necessarily to scale, emphasis instead generally being placed upon illustrative principles. The figures are to be considered illustrative in all aspects and are not intended to limit the invention, the scope of which is defined only by the claims.
The systems and methods disclosed herein describe detecting and analyzing features of an artery using intravascular data including scan lines and images generated using scan lines or other data obtained with regard to the artery. In one embodiment, the intravascular data is analyzed and transformed to detect metal stent struts that block, cage, or otherwise “jail” a side branch of an artery. The intravascular data can include, for example, optical coherence tomography (OCT) or intravascular ultrasound (IVUS) data or other images of a blood vessel of interest. The intravascular data can be analyzed to identify sparse intensity peaks along each scan line—i.e., peaks that are surrounded by dark regions corresponding to a side branch which appears as a large shadow in most cases. In many cases a side branch manifests as an opening of the tissue region in the 2-D cross sectional view. As a consequence of this, there will be no shadows cast by the struts which jail the side branch.
In one embodiment, a sparse peak is characterized by analyzing image statistics along the scan line to check if there is evidence of a bright signal against a dark background. A threshold T or Ts, also referred to as a naïve peak at line measurement threshold is then applied on the image statistics to check if the scan lines are candidates for a potential metal strut. Consecutive scan lines, or portions thereof, are analyzed to determine whether they fit an intensity profile consistent with a metal strut in one embodiment. Other thresholds and metrics can be used to filter and select side branch associated scan lines to identify candidates for subsequent validation. In some implementations further validation after scan line identification is not required.
As shown, the catheter 20 is introduced into the lumen 11 such as an arterial lumen. The probe 7 can include a rotating or slidable fiber 15 that directs light forward into the lumen 14 or at a direction perpendicular to the longitudinal axis of the fiber 15. As a result, in the case of light that is directed from the side of the probe as the fiber 15 rotates, OCT data is collected with respect to the walls of the blood vessel 5. The walls of the blood vessel 5 define a lumen boundary. This lumen boundary can be detected using the distance measurements obtained from the optical signals collected at the probe tip 17 using lumen detection software component. Side branches and stent struts and other features can be identified in the scan lines generated during a pullback through the artery by the probe. The probe 7 can include other imaging modalities in addition to OCT such as ultrasound in one embodiment.
As shown in
In one embodiment, an optical receiver 31 such as a balanced photodiode based system can receive light exiting the probe 7. A computing device 40 such as a computer, processor, ASIC or other device can be part of the OCT system 10 or can be included as a separate subsystem in electrical or optical communication with the OCT system 10. The computing device 40 can include memory, storage, buses and other components suitable for processing data and software 44 such as image data processing stages configured for side branch detection, stent strut candidate selection or identification, stent strut validation, correlations and comparisons of stent image data stent visualization, and pullback data collection as discussed below. In one embodiment, the software 44 can include a pipeline that includes various modules such as a jailed side branch/stent detection module. The module can include various other software modules such as a sparse peak detection module, model strut generation module, false positive testing module, and others as described herein.
In one embodiment, the computing device 40 includes or accesses software modules or programs 44, such as a side branch detection module, a lumen detection module, a stent detection module, a stent strut validation module, a candidate stent strut identification module and other software modules. The software modules or programs 44 can include an image data processing pipeline or component modules thereof and one or more graphical user interfaces (GUI). The modules can be subsets of each other and arranged and connected through various inputs, outputs, and data classes.
An exemplary image processing pipeline and components thereof can constitute one or more of the programs 44. The software modules or programs 44 receive image data and transform such image data into two dimensional and three dimensional views of blood vessels and stents can include lumen detection software module, peak detection, stent detection software module, side branch detection software module and a jailed or blocked side branch module. The image data processing pipeline, its components software modules and related methods and any of the methods described herein are stored in memory and executed using one or more computing devices such as a processor, device, or other integrated circuit.
As shown, in
In addition, this information 47 can include, without limitation, cross-sectional scan data, longitudinal scans, diameter graphs, image masks, stents, areas of malapposition, lumen border, and other images or representations of a blood vessel or the underlying distance measurements obtained using an OCT system and data collection probe. The computing device 40 can also include software or programs 44, which can be stored in one or more memory devices 45, configured to identify stent struts and malapposition levels (such as based on a threshold and measured distance comparison) and other blood vessel features such as with text, arrows, color coding, highlighting, contour lines, or other suitable human or machine readable indicia.
Once the OCT data is obtained with a probe and stored in memory; it can be processed to generate information 47 such as a cross-sectional, a longitudinal, and/or a three-dimensional view of the blood vessel along the length of the pullback region or a subset thereof. These views can be depicted as part of a user interface as shown in
Also visible in
In
Thus, there are no shadows associated with these struts in OCT image data. However, using the detection methods described herein, these jailing struts are detectable.
The image of
Once detected, the struts can be displayed on a user interface, which conveys vital information to the clinician about the precise location of stent struts and whether adjustments may be necessary to optimize stent placement and reduce the risk of side effects. The presence of jailing struts over a side branch is an important input for treatment, and in some cases additional interventions can be executed to mitigate the negative effects resulting from the jailed sidebranch. The user interface can include cross-sectional images, L-Mode images, A-Line images, three dimensional renderings, or any other suitable display format for visualizing detected struts.
At a high level, the methods disclosed herein detect jailing struts in OCT image data by detecting bright spots that are bordered by dark regions. Stent struts, and bare metal stent struts in particular, reflect the coherent light used in OCT imaging. The methods described herein can be used with stent struts that can be detected in an intravascular image. In one embodiment, the struts are metal struts such as bare metal struts “BMS” for example. However, blood vessel tissues, lipid plaques, and other intravascular features also reflect coherent light, making it difficult to distinguish struts in OCT images based on reflectivity alone. Further, as noted above, shadows cast by jailing struts are not detectable against the backdrop of a side branch lumen. To solve this problem, an algorithm called Naïve Peak at Line Measurement (NPLM) is provided for detecting jailing struts.
The first step 110 of the method 100 is to compute the peak-at-line intensity (i.e., maximum intensity) for each scan line that corresponds to a side branch in the pullback data. Scan lines corresponding side branches are extracted from the original, raw image data 120 and side branch data 130 gathered during the imaging process. The raw image data can be of various types and formats. For example, the raw image data can be scan lines, 8 bit data, 16 bit data, 32 bit data, and other data formats. The original, raw image data 120 include the OCT scan lines. The side branch data 130 include the locations of side branches in the OCT pullback. Methods, systems, and devices for detecting side branches are known such as described in U.S. Pat. No. 8,831,321, the contents of which are incorporated by reference in its entirety.
At Step 140, each side branch scan line is partitioned into a plurality of “samples”, and the samples are subsequently analyzed for brightness. In one embodiment, the analysis uses the portion of the scan-line beyond the imaging catheter and up to a certain depth beyond the sidebranch ostium (if known).
At Step 150, the samples are analyzed to count those samples with intensity above a pre-determined threshold on an image statistic along the scan-line. The threshold on the selected image statistic can vary for each scan line. For example, the threshold intensity can be a function of the maximum peak intensity for a given scan line, and samples from that scan line can be compared against the scan-line-specific peak intensity. Alternatively, the same threshold intensity can be used to analyze samples from different scan lines.
In one embodiment, the threshold intensity is scan-line-specific and corresponds to the peak intensity detected at the scan-line, and samples from a given scan line are screened to identify the number of samples having an intensity greater than about 10% of the peak-at-line intensity (i.e., 0.1×peak-at-line) for that particular scan line. In one embodiment, the screening of the samples to limit the result to a threshold proportional to the peak-at-line intensity generates a result that is equivalent to the maximum peak on that line. In one embodiment, the threshold varies for each scanline. In one embodiment, the measurement of peak intensity varies from scanline to scanline which yields a threshold value.
At Step 160, the number of samples calculated in Step 150 is compared against an empirically determined threshold, or NPLM threshold. The NPLM threshold is based on an upper bound on the strut blooming manifested on the OCT image. In one embodiment, the NPLM threshold is set on a per imaging system basis. The threshold can be set empirically by establishing a sensitivity level and adjusting the parameters of the strut detection method accordingly. If the number of samples calculated in Step 150 is less than or equal to the NPLM threshold, then the scan line is flagged as containing a potential strut and the process continues to Step 170.
As noted above, jailing struts appear as sparse peaks in the scan lines against the dark backdrop of side branches. The NPLM threshold tests the scan line profile to confirm the sharpness and overall width of an intensity peak(s). If too many samples exceed the threshold, then the “no” path is followed to Step 165 in which the scan line is then discarded as likely not containing a jailing strut or it is penalized (i.e., set aside) until/unless it is apparent that the penalized scan line is part of a continuous block of flagged scan lines.
At Step 170, neighboring flagged scan lines are clustered into contiguous blocks. The strut region is defined as a number of consecutive scan lines that qualified under the NPLM threshold. A tentative final location (in terms of A-Line and offset) is also determined for each strut.
At Step 180, after identifying potential struts and their locations, struts optionally can be vetted to determine whether they are true positives or false positives. In various embodiments, the line profile of a detected strut is compared to the profile of a “model” strut at the detected location using a linear correlation coefficient as the comparison metric. A model strut profile is created as a sharp peak with the same peak intensity as the detected strut and at the same location on the scan line as the detected strut. Correlation coefficients measure the association or similarity between two vectors or variables. Here, the correlation coefficient is defined as:
If the correlation coefficient is greater than an empirically determined threshold, which is determined based on multiple datasets and experimental analysis, then the detected strut is deemed a true positive and are added to a list of detected struts (Step 190). If the correlation coefficient is less than an empirically determined threshold, then the detected strut is penalized or discarded.
Some portions of the detailed description are presented in terms of algorithms and symbolic representations of operations on data bits within a computer memory. These algorithmic descriptions and representations can be used by those skilled in the computer and software related fields. In one embodiment, an algorithm is here, and generally, conceived to be a self-consistent sequence of operations leading to a desired result. The operations performed as methods stops or otherwise described herein are those requiring physical manipulations of physical quantities. Usually, though not necessarily, these quantities take the form of electrical or magnetic signals capable of being stored, transferred, combined, transformed, compared, and otherwise manipulated.
The algorithms and displays presented herein are not inherently related to any particular computer or other apparatus. Various general purpose systems may be used with programs in accordance with the teachings herein, or it may prove convenient to construct more specialized apparatus to perform the required method steps. The required structure for a variety of these systems will appear from the description below.
Embodiments of the invention may be implemented in many different forms, including, but in no way limited to, computer program logic for use with a processor (e.g., a microprocessor, microcontroller, digital signal processor, or general purpose computer), programmable logic for use with a programmable logic device, (e.g., a Field Programmable Gate Array (FPGA) or other PLD), discrete components, integrated circuitry (e.g., an Application Specific Integrated Circuit (ASIC)), or any other means including any combination thereof. In a typical embodiment of the present invention, some or all of the processing of the data collected using an OCT probe, an FFR probe, an angiography system, and other imaging and subject monitoring devices and the processor-based system is implemented as a set of computer program instructions that is converted into a computer executable form, stored as such in a computer readable medium, and executed by a microprocessor under the control of an operating system. Thus, user interface instructions, detection steps and triggers based upon the completion of a pullback or a co-registration request, for example, are transformed into processor understandable instructions suitable for generating OCT data, detecting struts, validating struts, display detected and validated struts and performing image procession using various and other features and embodiments described above.
Computer program logic implementing all or part of the functionality previously described herein may be embodied in various forms, including, but in no way limited to, a source code form, a computer executable form, and various intermediate forms (e.g., forms generated by an assembler, compiler, linker, or locator). Source code may include a series of computer program instructions implemented in any of various programming languages (e.g., an object code, an assembly language, or a high-level language such as Fortran, C, C++, JAVA, or HTML) for use with various operating systems or operating environments. The source code may define and use various data structures and communication messages. The source code may be in a computer executable form (e.g., via an interpreter), or the source code may be converted (e.g., via a translator, assembler, or compiler) into a computer executable form.
The computer program may be fixed in any form (e.g., source code form, computer executable form, or an intermediate form) either permanently or transitorily in a tangible storage medium, such as a semiconductor memory device (e.g., a RAM, ROM, PROM, EEPROM, or Flash-Programmable RAM), a magnetic memory device (e.g., a diskette or fixed disk), an optical memory device (e.g., a CD-ROM), a PC card (e.g., PCMCIA card), or other memory device. The computer program may be fixed in any form in a signal that is transmittable to a computer using any of various communication technologies, including, but in no way limited to, analog technologies, digital technologies, optical technologies, wireless technologies (e.g., Bluetooth), networking technologies, and internetworking technologies. The computer program may be distributed in any form as a removable storage medium with accompanying printed or electronic documentation (e.g., shrink-wrapped software), preloaded with a computer system (e.g., on system ROM or fixed disk), or distributed from a server or electronic bulletin board over the communication system (e.g., the internet or World Wide Web).
Hardware logic (including programmable logic for use with a programmable logic device) implementing all or part of the functionality previously described herein may be designed using traditional manual methods, or may be designed, captured, simulated, or documented electronically using various tools, such as Computer Aided Design (CAD), a hardware description language (e.g., VHDL or AHDL), or a PLD programming language (e.g., PALASM, ABEL, or CUPL).
Programmable logic may be fixed either permanently or transitorily in a tangible storage medium, such as a semiconductor memory device (e.g., a RAM, ROM, PROM, EEPROM, or Flash-Programmable RAM), a magnetic memory device (e.g., a diskette or fixed disk), an optical memory device (e.g., a CD-ROM), or other memory device. The programmable logic may be fixed in a signal that is transmittable to a computer using any of various communication technologies, including, but in no way limited to, analog technologies, digital technologies, optical technologies, wireless technologies (e.g., Bluetooth), networking technologies, and internetworking technologies. The programmable logic may be distributed as a removable storage medium with accompanying printed or electronic documentation (e.g., shrink-wrapped software), preloaded with a computer system (e.g., on system ROM or fixed disk), or distributed from a server or electronic bulletin board over the communication system (e.g., the internet or World Wide Web).
Various examples of suitable processing modules are discussed below in more detail. As used herein a module refers to software, hardware, or firmware suitable for performing a specific data processing or data transmission task. In one embodiment, a module refers to a software routine, program, or other memory resident application suitable for receiving, transforming, routing and processing instructions, or various types of data such as angiography data, OCT data, IVUS data, peak intensity, adaptive thresholds, and other information of interest as described herein.
Computers and computer systems described herein may include operatively associated computer-readable media such as memory for storing software applications used in obtaining, processing, storing and/or communicating data. It can be appreciated that such memory can be internal, external, remote or local with respect to its operatively associated computer or computer system.
Memory may also include any means for storing software or other instructions including, for example and without limitation, a hard disk, an optical disk, floppy disk, DVD (digital versatile disc), CD (compact disc), memory stick, flash memory, ROM (read only memory), RAM (random access memory), DRAM (dynamic random access memory), PROM (programmable ROM), EEPROM (extended erasable PROM), and/or other like computer-readable media.
In general, computer-readable memory media applied in association with embodiments of the invention described herein may include any memory medium capable of storing instructions executed by a programmable apparatus. Where applicable, method steps described herein may be embodied or executed as instructions stored on a computer-readable memory medium or memory media. These instructions may be software embodied in various programming languages such as C++, C, Java, and/or a variety of other kinds of software programming languages that may be applied to create instructions in accordance with embodiments of the invention.
The aspects, embodiments, features, and examples of the invention are to be considered illustrative in all respects and are not intended to limit the invention, the scope of which is defined only by the claims. Other embodiments, modifications, and usages will be apparent to those skilled in the art without departing from the spirit and scope of the claimed invention.
The use of headings and sections in the application is not meant to limit the invention; each section can apply to any aspect, embodiment, or feature of the invention.
Throughout the application, where compositions are described as having, including, or comprising specific components, or where processes are described as having, including or comprising specific process steps, it is contemplated that compositions of the present teachings also consist essentially of, or consist of, the recited components, and that the processes of the present teachings also consist essentially of, or consist of, the recited process steps.
In the application, where an element or component is said to be included in and/or selected from a list of recited elements or components, it should be understood that the element or component can be any one of the recited elements or components and can be selected from a group consisting of two or more of the recited elements or components. Further, it should be understood that elements and/or features of a composition, an apparatus, or a method described herein can be combined in a variety of ways without departing from the spirit and scope of the present teachings, whether explicit or implicit herein.
The use of the terms “include,” “includes,” “including,” “have,” “has,” or “having” should be generally understood as open-ended and non-limiting unless specifically stated otherwise.
The use of the singular herein includes the plural (and vice versa) unless specifically stated otherwise. Moreover, the singular forms “a,” “an,” and “the” include plural forms unless the context clearly dictates otherwise. In addition, where the use of the term “about” is before a quantitative value, the present teachings also include the specific quantitative value itself, unless specifically stated otherwise. As used herein, the term “about” refers to a ±10% variation from the nominal value.
It should be understood that the order of steps or order for performing certain actions is immaterial so long as the present teachings remain operable. Moreover, two or more steps or actions may be conducted simultaneously.
Where a range or list of values is provided, each intervening value between the upper and lower limits of that range or list of values is individually contemplated and is encompassed within the invention as if each value were specifically enumerated herein. In addition, smaller ranges between and including the upper and lower limits of a given range are contemplated and encompassed within the invention. The listing of exemplary values or ranges is not a disclaimer of other values or ranges between and including the upper and lower limits of a given range.
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